Question: The sum of two numbers is $27$, and their difference is $3$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 27}$ ${x-y = 3}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 30 $ $ x = \dfrac{30}{2} $ ${x = 15}$ Now that you know ${x = 15}$ , plug it back into $ {x+y = 27}$ to find $y$ ${(15)}{ + y = 27}$ ${y = 12}$ You can also plug ${x = 15}$ into $ {x-y = 3}$ and get the same answer for $y$ ${(15)}{ - y = 3}$ ${y = 12}$ Therefore, the larger number is $15$, and the smaller number is $12$.